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NASA NTRS1982

The dynamic flexural response of propeller blades

The determination of the torsional constants of three blade models having NACA four-digit symmetrical airfoil cross sections is presented. Values were obtained for these models analytically and experimentally. Results were also obtained for three other models having rectangular, elliptical, and parabolic cross sections. Complete modal analyses were performed for five blade models. The identification of modal parameters was done for cases when the blades were modeled as either undamped or damped multi-degree-of-freedom systems. For the experimental phase of this study, the modal testing was performed using a Dual Channel FFT analyzer and an impact hammer (which produced an impulsive excitation). The natural frequency and damping of each mode in the frequency range up to 2 kHz were measured. A small computer code was developed to calculate the dynamic response of the blade models for comparison with the experimental results. A comparison of the undamped and damped cases was made for all five blade models at the instant of maximum excitation force. The program was capable of handling models where the excitation forces were distributed arbitrarily along the length of the blade.

Djordjevic, S. Z.↗

NASA NTRS2000

Ground Vibration Test Planning and Pre-Test Analysis for the X-33 Vehicle

This paper describes the results of the modal test planning and the pre-test analysis for the X-33 vehicle. The pre-test analysis included the selection of the target modes, selection of the sensor and shaker locations and the development of an accurate Test Analysis Model (TAM). For target mode selection, four techniques were considered, one based on the Modal Cost technique, one based on Balanced Singular Value technique, a technique known as the Root Sum Squared (RSS) method, and a Modal Kinetic Energy (MKE) approach. For selecting sensor locations, four techniques were also considered; one based on the Weighted Average Kinetic Energy (WAKE), one based on Guyan Reduction (GR), one emphasizing engineering judgment, and one based on an optimum sensor selection technique using Genetic Algorithm (GA) search technique combined with a criteria based on Hankel Singular Values (HSV's). For selecting shaker locations, four techniques were also considered; one based on the Weighted Average Driving Point Residue (WADPR), one based on engineering judgment and accessibility considerations, a frequency response method, and an optimum shaker location selection based on a GA search technique combined with a criteria based on HSV's. To evaluate the effectiveness of the proposed sensor and shaker locations for exciting the target modes, extensive numerical simulations were performed. Multivariate Mode Indicator Function (MMIF) was used to evaluate the effectiveness of each sensor & shaker set with respect to modal parameter identification. Several TAM reduction techniques were considered including, Guyan, IRS, Modal, and Hybrid. Based on a pre-test cross-orthogonality checks using various reduction techniques, a Hybrid TAM reduction technique was selected and was used for all three vehicle fuel level configurations.

Bedrossian, Herand↗

NASA NTRS1982

Modal vector estimation for closely spaced frequency modes

Techniques for obtaining improved modal vector estimates for systems with closely spaced frequency modes are discussed. In describing the dynamical behavior of a complex structure modal parameters are often analyzed: undamped natural frequency, mode shape, modal mass, modal stiffness and modal damping. From both an analytical standpoint and an experimental standpoint, identification of modal parameters is more difficult if the system has repeated frequencies or even closely spaced frequencies. The more complex the structure, the more likely it is to have closely spaced frequencies. This makes it difficult to determine valid mode shapes using single shaker test methods. By employing band selectable analysis (zoom) techniques and by employing Kennedy-Pancu circle fitting or some multiple degree of freedom (MDOF) curve fit procedure, the usefulness of the single shaker approach can be extended.

Craig, R. R., Jr.↗

NASA NTRS1993

An overview of recent advances in system identification

This paper presents an overview of the recent advances in system identification for modal testing and control of large flexible structures. Several techniques are discussed including the Observer/Kalman Filter Identification, the Observer/Controller Identification and the State-Space System Identification in the Frequency Domain. The System/Observer/Controller Toolbox developed at NASA Langley Research Center is used to show the applications of these techniques to real aerospace structures such as the Hubble spacecraft telescope and the active flexible aircraft wing.

Juang, Jer-Nan↗

NASA NTRS1994

An overview of recent advances in system identification

This paper presents an overview of the recent advances in system identification for modal testing and control of large flexible structures. Several techniques are discussed including the Observer/Kalman Filter Identification, the Observer/Controller Identification, and the State-Space System Identification in the Frequency Domain. The System/Observer/Controller Toolbox developed at NASA Langley Research Center is used to show the applications of these techniques to real aerospace structures such as the Hubble spacecraft telescope and the active flexible aircraft wing.

Juang, Jer-Nan↗

NASA NTRS1987

The measurement and control of helicopter blade modal response using blade-mounted accelerometers

The measurement of helicopter blade flapping, bending, and lag modal acceleration and displacement response using blade-mounted accelerometers is described. It is shown that knowledge of the blade mode shapes is sufficient to permit separation of the modal contributions to the accelerometer signals using matrix inversion. The application of the Mckillip (1985) filter to the identification of modal rate response is described. Finally, the design of flapping, bending, and lag mode controllers utilizing the conventional mesh plate is presented. The measurement technique is illustrated using flight test results obtained using a Black Hawk helicopter.

Ham, Norman D.↗

NASA NTRS1979

On adaptive modal control of large flexible spacecraft

A recently developed strategy for adaptive sampled-data control of distributed parameter systems based on a plant modal expansion description and modal simultaneous identification and regulation algorithms is presented with frequent reference to the annular momentum control device (AMCD) test example. The requirements of observation spillover reduction and modal eigenvector shape prespecification, which are especially crucial to the proposed adaptive control strategy, are addressed. Individual low pass time filtering of sensed AMCD particle displacements is proposed for observation spillover reduction. A layered scheme incorporating 'eigenvector' shape improvement is outlined to combat the expansion basis prespecification requirement.

Johnson, C. R., Jr.↗

NASA NTRS1986

Effects of noise on modal parameters identified by the Eigensystem Realization Algorithm

The basic concept of the Eigensystem Realization Algorithm for modal parameter identification and model reduction is extended to minimize the distortion of the identified parameters caused by noise. The mathematical foundation for the properties of accuracy indicators, such as the singular values of the data matrix and modal amplitude coherence, is provided, based on knowledge of the noise characteristics. These indicators quantitatively discriminate noise from system information and are used to reduce the realized system model to a better approximation of the true model. Monte Carlo Simulations are included to support the analytical studies.

Juang, J.-N.↗

NASA NTRS1986

Effects of noise on ERA-identified modal parameters

The basic concept of the Eigensystem Realization Algorithm (ERA) for modal parameter identification and model reduction is extended to minimize the distortion of the identified parameters caused by noise. The mathematical foundation for the properties of accuracy indicators such as the singular values of the data matrix and modal amplitude coherence is provided based on knowledge of the noise characteristics. These indicators quantitatively discriminate noise from system information and are used to reduce the realized system model to a better approximation of the true model. Monte Carlo simulations are included to support the analytical studies.

Juang, J.-N.↗

NASA NTRS1988

Optimal experiment design for identification of large space structures

The optimal experiment design for on-orbit identification of modal frequency and damping parameters in large flexible space structures is discussed. The main result is a separation principle for D-optimal design which states that under certain conditions the sensor placement problem is decoupled from the input design problem. This decoupling effect significantly simplifies the overall optimal experiment design determination for large MIMO structural systems with many unknown modal parameters. The error from using the uncoupled design is estimated in terms of the inherent damping of the structure. A numerical example is given, demonstrating the usefulness of the simplified criteria in determining optimal designs for on-orbit Space Station identification experiments.

Bayard, D. S.↗

NASA NTRS2013

Progress in Operational Analysis of Launch Vehicles in Nonstationary Flight

This paper presents recent results in an ongoing effort to understand and develop techniques to process launch vehicle data, which is extremely challenging for modal parameter identification. The primary source of difficulty is due to the nonstationary nature of the situation. The system is changing, the environment is not steady, and there is an active control system operating. Hence, the primary tool for producing clean operational results (significant data lengths and data averaging) is not available to the user. This work reported herein uses a correlation-based two step operational modal analysis approach to process the relevant data sets for understanding and development of processes. A significant drawback for such processing of short time histories is a series of beating phenomena due to the inability to average out random modal excitations. A recursive correlation process coupled to a new convergence metric (designed to mitigate the beating phenomena) is the object of this study. It has been found in limited studies that this process creates clean modal frequency estimates but numerically alters the damping.

James, George↗

NASA NTRS1990

An experimental modal testing/identification technique for personal computers

A PC-based system for mode shape identification is evaluated. A time-domain modal identification procedure is utilized to identify the mode shapes of a beam apparatus from discrete time-domain measurements. The apparatus includes a cantilevered aluminum beam, four accelerometers, four low-pass filters, and the computer. The method's algorithm is comprised of an identification algorithm: the Eigensystem Realization Algorithm (ERA) and an estimation algorithm called Minimum Model Error (MME). The identification ability of this algorithm is compared with ERA alone, a frequency-response-function technique, and an Euler-Bernoulli beam model. Detection of modal parameters and mode shapes by the PC-based time-domain system is shown to be accurate in an application with an aluminum beam, while mode shapes identified by the frequency-domain technique are not as accurate as predicted. The new method is shown to be significantly less sensitive to noise and poorly excited modes than other leading methods. The results support the use of time-domain identification systems for mode shape prediction.

Roemer, Michael J.↗

NASA NTRS1976

Identification of natural frequencies and modal damping ratios of aerospace structures from response data

An analysis of one and multidegree of freedom systems with classical damping is presented. Definition and minimization of error functions for each system are discussed. Systems with classical and nonclassical normal modes are studied, and results for first order perturbation are given. An alternative method of matching power spectral densities is provided, and numerical results are reviewed.

Michalopoulos, C. D.↗

NASA NTRS1982

An approximation theory for nonlinear partial differential equations with applications to identification and control

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Banks, H. T.↗

NASA NTRS1985

An Eigensystem Realization Algorithm for Application to Modal Testing

Important features of the Eigensystem Realization Algorithm (ERA) are summarized as follows: (1) from the computational standpoint, the algorithm is attractive, since only simple numerical operations are needed; (2) the computational procedure is numerically stable; (3) the structural dynamics requirements for modal parameter identification and the control design requirements for a reduced-state space model are satisfied; (4) data from more than one test can be used simultaneously to efficiently identify the closely spaced eigenvalues; and (5) no restrictions on number of measurements are imposed.

Juang, J. N.↗

NASA NTRS1985

On-orbit parameter and disturbance identification for Space Station

This paper describes recent efforts directed at the problem of on-orbit parameter and disturbance identification for the Space Station. Techniques are developed for identification of rigid body parameters, flexible body parameters, and quasi-static disturbances relevant to the Power Tower configuration currently under investigation by NASA. The paper concludes with a case study investigating the identification of modal frequencies in a 15 degree of freedom planar model of the Space Station under a variety of operational settings.

Bayard, D. S.↗

NASA NTRS1988

Some experiences with the Eigensystem Realization Algorithm

The Eigensystem Realization Algorithm (ERA) is a multiinput/multioutput time-domain algorithm for minimum-order system realization and modal parameter identification. It has been used for structural dynamics data analysis at the Langley Research Center for several years. Some of the practical experiences encountered in these projects are discussed in this paper. Three examples are used: the Galileo spacecraft, the Solar Array Flight Experiment, and a laboratory space-truss model. Several techniques for assessing identification accuracy are illustrated.

Pappa, Richard S.↗

NASA NTRS1989

Recursive form of the eigensystem realization algorithm for system identification

An algorithm is developed for recursively calculating the minimum realization of a linear system from sampled impulse response data. The Gram-Schmidt orthonormalization technique is used to generate an orthonormal basis for factorization of the data matrix. The system matrix thus identified is in upper Hessenberg form, which has advantages for the identification of modal parameters including damping coefficients, frequencies, mode shapes, and modal participation factors. It also has the property that once an element of the system matrix is computed, it is never altered as the dimension of the model is increased in the recursive process. Numerical examples are presented for comparison of the recursive and nonrecursive forms of the eigensystem realization algorithm.

Longman, Richard W.↗